Electrical bridge



y 3, 1962 R. 1.. KONIGSBERG 3,034,044

ELECTRICALBRIDGE Filed Dec. 4, 1957 UNKNOWN I L5 VOLTS v A e STANDARDUNKNOWN z 4 1.5 VOLTS 5 1/ FIG. 2. STANDARD ROBERT L. KONIGSBERGINVENTOR ATTORNEYS United States Patent M 3,934,044 ELECTRICAL BRWQERobert L. Konigsherg, Baltimore, Md, assignor to the United States of Aneriea as represented by the beerstary of the Navy Fiied Dec. 4, 1957,Ser. No. 709,729 3 tliaims. (iii. 324-57) The present invention relatesto an electrical bridge; more particularly it relates to an improved lowfrequency bridge of the operational type, useful for the measurement ofhigh capacitances with small dissipation factors.

In certain control system applications operational amplifiers areemployed in integrating circuits at very low frequencies. Theintegrating network generally consists of a resistance in series withthe amplifier input and a capacitor connected between amplifier outputand input. tively high, for example up to 30 paid. in some applications.zant of the low frequency (.05 to c.p.s.) performance and thetemperature characteristics of the integrating capacitor The principalobject of the present invention therefore, is to provide an electricalbridge ,which will permit measurements of capacitances (or resistances)at very low frequencies and with a high degree of accuracy Anotherimportant object of the invention is to provide an electrical bridgewhich will afiord high output current sensitivity at bridge balanceespecially at low frequencies where the conventional four arm passivebridge is relatively insensitive Another object resides in the provisionof an electrical bridge which will be D.C. stabilized in use,particularly during low frequency measurements.

As further objects, the invention provides an electrical bridge whereinthe inherent noise is maintained at a low level and does not affectsettings for bridge balance, and in which distortion is maintained at aninsignificant level.

Another object of the invention is to provide an electrical bridgewhich, with certain modifications, may be used for accurately measuringhigh values of inductance.

And the invention provides, as a further object, an electrical bridgewhich may be adapted for producing accurate measurements of resistanceand temperature coefficients of resistance in the very low frequencyrange (.05 to 10 c.p.s.).

Other objects and many of the attendant advantages of this inventionwill be readily appreciated as the same becomes better understood byreference to the following.

detailed description when considered in connection with the accompanyingdrawings, wherein:

FIG. 1 is a circuit'schematic of the improved electrical bridgeconstituting the present invention;

FIG. 2 is a circuit schematic of the invention modified to permit themeasurement of inductance.

Referring to the drawings and first to FIG. 1 a source of low frequencyvoltage such as a signal generator, is

For accurate results it is desirable to be cogni- Capacitance values inthe network may be relashown at 10. One terminal of the signal generatoris connected to ground, as designated at 11.

One arm of the improved bridge includes the unknown impedance Z which isconstituted by a capacitor C and a resistor R connected in series. Theadjacent arm of the bridge includes a known value (standard) capacitor Cand a variable resistor R also of known range, connected in series. isconnected to the junction of the adjacent bridge arms, just described,at point e The arm of the bridge which includes the unknown impedancealso includes an operational amplifier A, which is shunted by a variableresistor R the amplifier having a terminal connected to ground 11.Similarly, the arm of the bridge including 3,034,044 Patented May 8,1962

the known impedance also includes an operational amplifier A which isshunted by a resistor R the amplifier A also having a terminal connectedto ground. A meter M is connected to the junctions 12 and 13, that is tothe operational amplifier outputs, and is shunted by a suitable metersensitivity control, shown as a potentiometer 14. Any initial D.C.unbalance between amplifier outputs, which is generally in the millivoltregion, may be compensated for by adjustment of potentiometers 15 and16. More specifically, the resistor elements of the potentiometers 15and 16 areconnected in series relation with batteries 17 and 18, asshown in FIG. 1, with the aim of the potentiometer 15 connected to thejunction 12 and the arm of the potentiometer 16 connected to a terminalof the meter M. Bridge A.C. balance is obtained by varying resistors Rand R The bridge balance equation may bearrived at in the followingmanner (refer to FIG. 1). It can be shown, using Kirchoffs laws andassuming the output loop open circuited, that am Eu (1) 1 x Where:

At bridge A.C. balance, indicated by zero deflection of the output meterM,

Substituting Equations '1 and 2 in Equation 3, assummg K and K are bothunity and equating real and imaginary terms, solving for R and C Theeffectiveness of Equations 4 and 5 for calculating the unknownresistance (R and the unknown capacity (C is related to the gain of theoperational amplifiers A and A In general, accuracy will improve asamplifier gain increases, as output impedance decreases and as inputimpedance approaches infinity. In a test experiment the gain of theamplifiers A and A was of the order of 100,000 at .05 c.p.s., fallingoff to about 1,000 at 10 c.p.s. This decrease in :gain had a secondorder effect on accuracy of the measurement of capacitance and a firstorder effect on the accuracy of measurement of the dissipation factor(the dissipation factor where d =dissipation factor in the standard armof the bridge and w angular frequency).

Dissipation factor measurement accuracy deteriorates at 10 c.p.s. andmay become as high as 50%. However, an overall capacitance measurementaccuracy of i 2.5% is readily achievable in the .05 to 10 c.p.s. rangewhile v 3 V accuracies of the order of can be realized for dissipationfactor in the .05 to 2 c.p.s. range.

Accuracy of a bridge constructed as described hereinabove is limitedonly by the following factors, assuming that the standard impedance isknown accurately: (a) gain, input and outputimpedances of theoperational arnplifieris;(b) the relative magnitudesv of strayimpedances;

(c) the ratio of the respective changes in meteredo'utput current ,tochanges in the parameters (in values of ,resistors R and R about thebridge balance point, (i.e., bridge balance sensitivities); (d) theinherent noise in troduced into ,the metering vcircuit by theoperational' amplifiers A; and A -(e) (the .purity of waveform of thesignal generator and the linearity oithe amplifiers; (g) the effect of.i'rnpure resistors R and R i.e.,

-whether ornotsaid resistors possess reactive components. 7 "The valueof an unknown inductor, shown at Z- in FIG. '2, may lac-determined bythe use of the improved bridgecircuit. More specifically, in FIG.,2, theinductor Z which consists ofthe inductance L in series with 1ts losscomponent R both of unknown value, is connected in shunt across theamplifier A For the em- I, bodiment shown in FIG. 2 the bridge balanceequation may'be arrived at in a manner generally similar to the equationfor FIG. 1, as follows:

Where K K are constants which are functions of gain, inputiimpedance andoutput impedanceof the amplifiers A A (K K approach unity asgainincreases).

At bridge A.C. balance, indicated by zero deflection of the output meterM:

Substituting equations 6 and in ,3, assuming constants K3, K4 are bothunity and solving for R and L R =R RgG (G =conductance standard) Lx=. 12cs Where 1 ear -r,

and

x= xTifi x By altering the circuit slightly'so that all bridge arms are:

i o1 Z (RJ sem li (11a). '61.- 3KB l I Substituting equations 9'and 10in Equation 11 and solving for R Obviously many modifications andvariations of the present invention are possible in the light of theabove teachings. It is therefore to be understood that within the scopeof the appended claims the invention may be practiced otherwise than asspecifically described.

What is claimed is:

1. An electrical bridge formeasuring impedances, comprising a pair oiparallel arms, the first arm of which includes afirst stabilizedhighgainanalog type 11C. amplifier having the unknown impedance connected to theamplifier input and a first known variable resistor connected frorntheamplifier output to saidinput, the second arm of said parallel armsincluding a second stabilized high gain analog type D.C. amplifierhaving a known impedance connected to its input and a second knownvariable resistor connected from its output to its input, said parallelarms having va common input terminal for receiving a-low frequencyalternating test voltage, and currentibalance indicating means connectedfrom the output of said first amplifier to the output of said secondamplifier, said balance indicating means including a pair ofpotentiometers, and a pair of batteries coupled in series relationwiththe resistor elements of said otentiometers, said otentiometers havingtheir movable contacts connectedto the output of said amplifiers.

V, 2. An electrical bridge for measuring capacitance comprising a pairofparallel arms, the first arm of which includes a first stabilized highgain analog type D.C. amplifienhaving the unknown capacitor connected tothe amplifier input and a first known variable resistor connected fromthe amplifier output to said input, the second arm of said parallel armsincluding a second stabilized of otentiometers, a pair of batteriescoupled to the re-- sistor elements of said Potentiometers in seriesrelation, said potentiometers having their movable contacts connected tothe output of said amplifiers.

3. An electricalbridge for measuring inductance, comprising a pair ofparallel arms, the first arm of which includes a first high gain analogtype D.C. amplifier having a' first known variable resistor connected.to the input thereof and the unknown inductor connected from theoutput'to said amplifier input, the second arm of said parallel armsincluding a second high gain analog type D.C. amplifier having astandard impedance connected to the input thereof and a second knownresistor connected from said second amplifier output to its input,

Where K and K are constants similar to the constants K and K4.

said standard impedance including a known capacitor and a known variableresistor, said first and second arms being joined at a common inputterminal which is connected to a low frequency alternating test voltagesource, andcurrent balance indicating means connected from the output ofsaid first amplifier to the output of said second amplifier, saidbalance indicatingmeans including a pair of potentiometer-s, a pair ofbatteries coupled to the resistor elements of said potentiometers .inseries relation, said potentituneters having their movable contacts.connected to the output of said amplifiers.

References Cited in the file of this patent References Cited in the fileof this petent UNITED STATES PATENTS Wills Sept. 24, 1940 Herzog Mar. 7,1950 T aborsky May 9, 1950 6 i Bessey May 12, 1953 Branson Nov. 17, 1953McCollom et a1 Nov. 30, 1954 Bousman Sept. 27, 1955 Hayes Feb. 16, 1960

